For the matrix the set is the column space of A. The vector v = has [select all that apply] ✔ a unique solution ✔ infinitely many solutions Ono solution. A = 2-3 3 3-4 3 3 -3 0, S = {b € R³ : : b = Ax for some x y Z 2 -3 3 x 3 -4 3 y 3 -3 0 z belongs to this set whenever the augmented matrix XER³ R³} By row reducing, we find that saying v ES is equivalent to x, y and z satisfying a linear condition of the form ax+by+cz=0. Specifically, this condition is equivalent to z/3+y+x=0 a plane through the origin 团. In this case the column space of A is Note: • the Maple syntax for the equation ax+by+cz=0 is a*x+b*y+c*z=0 • make sure to explicitly specify multiplication using an asterisk *.
For the matrix the set is the column space of A. The vector v = has [select all that apply] ✔ a unique solution ✔ infinitely many solutions Ono solution. A = 2-3 3 3-4 3 3 -3 0, S = {b € R³ : : b = Ax for some x y Z 2 -3 3 x 3 -4 3 y 3 -3 0 z belongs to this set whenever the augmented matrix XER³ R³} By row reducing, we find that saying v ES is equivalent to x, y and z satisfying a linear condition of the form ax+by+cz=0. Specifically, this condition is equivalent to z/3+y+x=0 a plane through the origin 团. In this case the column space of A is Note: • the Maple syntax for the equation ax+by+cz=0 is a*x+b*y+c*z=0 • make sure to explicitly specify multiplication using an asterisk *.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please
![For the matrix
the set
is the column space of A. The vector v =
has [select all that apply]
✔a unique solution
✔ infinitely many solutions
Ono solution.
A =
S =
= {b € R³ : b =
b = Ax
In this case the column space of A is
2-3 3
3-4 3
3 -3 0
(-)
for some
belongs to this set whenever the augmented matrix
2 -3 3x
3-4 3 y
3 -3 0 z
¤ R³}
By row reducing, we find that saying v ES is equivalent to x,y and z satisfying a linear condition of the form
ax+by+cz = 0. Specifically, this condition is equivalent to
z/3 + y + x = 0
a plane through the origin
Note:
• the Maple syntax for the equation ax+by+cz = 0 is a*x+b*y+c*z=0
• make sure to explicitly specify multiplication using an asterisk *.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec42d8d2-a477-479e-a302-04e5263e200e%2Fce643331-d458-4d27-85d2-29ecc250f63f%2Fhx8owz_processed.png&w=3840&q=75)
Transcribed Image Text:For the matrix
the set
is the column space of A. The vector v =
has [select all that apply]
✔a unique solution
✔ infinitely many solutions
Ono solution.
A =
S =
= {b € R³ : b =
b = Ax
In this case the column space of A is
2-3 3
3-4 3
3 -3 0
(-)
for some
belongs to this set whenever the augmented matrix
2 -3 3x
3-4 3 y
3 -3 0 z
¤ R³}
By row reducing, we find that saying v ES is equivalent to x,y and z satisfying a linear condition of the form
ax+by+cz = 0. Specifically, this condition is equivalent to
z/3 + y + x = 0
a plane through the origin
Note:
• the Maple syntax for the equation ax+by+cz = 0 is a*x+b*y+c*z=0
• make sure to explicitly specify multiplication using an asterisk *.
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